1. 4.4 Proving triangles using ASA and AAS

2. Post 21 Angle-Side-Angle (ASA)  post If 2  s and the included side of one Δ are  to the corresponding  s and included side of another Δ, then the 2 Δs are .

3. A B C ) (( X Y Z )) ( If  A   Z,  C   X and seg. AC  seg. ZX, then Δ ABC  Δ ZYX.

4. Thm 4.5 Angle-Angle-Side (AAS)  thm. If 2  s and a non-included side of one Δ are  to the corresponding  s and non-included side of another Δ, then the 2 Δs are .

5. If  A   R,  C   S, and seg AB  seg QR, then ΔABC  ΔRQS. (( )) ) )A B C R S Q

6. Proof 1.  A   R,  C   S, seg AB  seg QR, 2.  B   Q 3. Δ ABC  Δ RQS 1. Given 2. 3 rd angles thm 3. ASA post

7. Examples Is it possible to prove the Δs are  ? ) )) ( (( No, there is no AAA thm! )) ( (( ) Yes, ASA

8. THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS

9. Example Given that  B   C,  D   F, M is the midpoint of seg DF Prove Δ BDM  Δ CFM B D M C F ) ) )) ((

10. Proof Statements 1. Given that  B  C,  D   F, M is the midpoint of seg DF 2. Seg DM  Seg MF 3. Δ BDM  Δ CFM Reasons 1. Given 2. Def of a midpoint 3. AAS thm

11. Example Given that seg WZ bisects  XZY and  XWY Prove that Δ WZX  Δ WZY (( ) ) X Z Y W

12. Proof Statements 1. seg WZ bisects  XZY and  XWY 2.  XZW  YZW,  XWZ   YWZ 3. Seg ZW  seg ZW 4. Δ WZX  Δ WZY Reasons 1. Given 2. Def  bisector 3. Reflex prop of seg  4. ASA post

13. 4.5 Using  Δs

14. Once you know that Δs are , you can state that their corresponding parts are .

15. CPCTC CPCTC-corresponding parts of  triangles are . Ex: G: seg MP bisects  LMN, seg LM  seg NM P: seg LP  seg NP ( ) N P L M

16. Proof: Statements 1. Seg MP bisects  LMN, seg LM  seg NM 2. Seg PM  seg PM 3. ΔPMN  ΔPML 4. Seg LP  seg NP Reasons 1.Given 2.Reflex. Prop seg  3.SAS post 4.CPCTC